Question 1

The limit of a function as x approaches c does not exist if the function approaches $- 5$ from the left of c and 4 from the right of

Accepted Answer

A) True 
 B)False

Question 2

Find $\lim _ { x \rightarrow + \infty } \frac { 1 - 2 x } { 1 + 3 x }$ (if it exists).

Accepted Answer

A) 0 
B)   $- \frac { 2 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D) -$\infty$ 
E) does not exist 
A) 0 
B)   $- \frac { 2 } { 3 }$ 
C)  $\frac { 2 } { 3 }$ 
D) -$\infty$ 
E) does not exist

Question 3

Find the limit (if it exists).  $\lim _ { x \rightarrow \infty } \left( \frac { 32 x - 1 } { 4 x + 4 } \right)$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 32 }$ 
C) 8 
D) -8 
E) does not exist 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 32 }$ 
C) 8 
D) -8 
E) does not exist

Question 4

Find the derivative of the function.  $h ( s ) = \frac { 1 } { \sqrt { s + 2 } }$

Accepted Answer

A)  $\frac { 1 } { 2 ( s - 2 ) ^ { \frac { 3 } { 2 } } }$ 
B)  $\frac { 1 } { 2 ( s + 2 ) ^ { \frac { 3 } { 2 } } }$ 
C)  $\frac { 1 } { ( s + 2 ) ^ { 2 } }$ 
D)  $\frac { 1 } { 2 \sqrt { s - 2 } }$ 
E)  $- \frac { 1 } { 2 ( s + 2 ) ^ { \frac { 3 } { 2 } } }$ 
A)  $\frac { 1 } { 2 ( s - 2 ) ^ { \frac { 3 } { 2 } } }$ 
B)  $\frac { 1 } { 2 ( s + 2 ) ^ { \frac { 3 } { 2 } } }$ 
C)  $\frac { 1 } { ( s + 2 ) ^ { 2 } }$ 
D)  $\frac { 1 } { 2 \sqrt { s - 2 } }$ 
E)  $- \frac { 1 } { 2 ( s + 2 ) ^ { \frac { 3 } { 2 } } }$

Question 5

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result.   $h ( x ) = \sqrt { x },(4,2)$

Accepted Answer

A)  $m = \frac { 1 } { 4 }$ 
B)  $m = - 2$ 
C)  $m = 4$ 
D)  $m = - \frac { 1 } { 4 }$ 
E)  $m = 2$ 
A)  $m = \frac { 1 } { 4 }$ 
B)  $m = - 2$ 
C)  $m = 4$ 
D)  $m = - \frac { 1 } { 4 }$ 
E)  $m = 2$

Question 6

Select the correct function for the graph using horizontal asymptotes as aids.

Accepted Answer

A)  $\frac { 6 x ^ { 2 } } { x ^ { 2 } + 8 }$ 
B)  $\frac { x ^ { 2 } } { x ^ { 2 } - 6 }$ 
C)  $\frac { x ^ { 2 } } { x ^ { 2 } + 6 }$ 
D)  $\frac { 8 x ^ { 2 } } { x ^ { 2 } + 6 }$ 
E)  $\frac { 8 x ^ { 2 } } { x ^ { 2 } - 6 }$ 
A)  $\frac { 6 x ^ { 2 } } { x ^ { 2 } + 8 }$ 
B)  $\frac { x ^ { 2 } } { x ^ { 2 } - 6 }$ 
C)  $\frac { x ^ { 2 } } { x ^ { 2 } + 6 }$ 
D)  $\frac { 8 x ^ { 2 } } { x ^ { 2 } + 6 }$ 
E)  $\frac { 8 x ^ { 2 } } { x ^ { 2 } - 6 }$

Question 7

Use the graph to determine the limit visually (if it exists).Then identify another function f2(x)that agrees with the given function at all but one point.
  $$f ( x ) = \frac { x ^ { 2 } - 1 } { x + 1 }$$       $\lim _ { x \rightarrow 2 } f ( x ) = ?$

Accepted Answer

A)  $f _ { 2 } ( x ) = x - 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 1$ 
B)  $f _ { 2 } ( x ) = 2 x - 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 3$ 
C)  $f _ { 2 } ( x ) = 2 x + 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 5$ 
D)  $f _ { 2 } ( x ) = x + 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 5$ 
E)  $f _ { 2 } ( x ) = x + 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 3$ 
A)  $f _ { 2 } ( x ) = x - 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 1$ 
B)  $f _ { 2 } ( x ) = 2 x - 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 3$ 
C)  $f _ { 2 } ( x ) = 2 x + 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 5$ 
D)  $f _ { 2 } ( x ) = x + 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 5$ 
E)  $f _ { 2 } ( x ) = x + 1$ $\lim _ { x \rightarrow 2 } f ( x ) = 3$

Question 8

Find the derivative of the function.   $f ( x ) = \frac { 1 } { x + 13 }$

Accepted Answer

A)  $- \frac { 1 } { ( x + 13 ) ^ { 2 } }$ 
B)  $- \frac { 1 } { 2 \sqrt { x + 13 } }$ 
C)  $\frac { 39 } { x ^ { 4 } }$ 
D)  $\frac { 1 } { ( x + 13 ) ^ { 2 } }$ 
E)  $\frac { 1 } { 2 \sqrt { x - 13 } }$ 
A)  $- \frac { 1 } { ( x + 13 ) ^ { 2 } }$ 
B)  $- \frac { 1 } { 2 \sqrt { x + 13 } }$ 
C)  $\frac { 39 } { x ^ { 4 } }$ 
D)  $\frac { 1 } { ( x + 13 ) ^ { 2 } }$ 
E)  $\frac { 1 } { 2 \sqrt { x - 13 } }$

Question 9

Select the correct function for the graph using horizontal asymptotes as aids.

Accepted Answer

A)  $\frac { 6 x ^ { 2 } } { x ^ { 2 } + 5 }$ 
B)  $\frac { 5 x ^ { 2 } } { x ^ { 2 } - 6 }$ 
C)  $\frac { x ^ { 2 } } { x ^ { 2 } - 6 }$ 
D)  $\frac { x ^ { 2 } } { x ^ { 2 } + 6 }$ 
E)  $\frac { 5 x ^ { 2 } } { x ^ { 2 } + 6 }$ 
A)  $\frac { 6 x ^ { 2 } } { x ^ { 2 } + 5 }$ 
B)  $\frac { 5 x ^ { 2 } } { x ^ { 2 } - 6 }$ 
C)  $\frac { x ^ { 2 } } { x ^ { 2 } - 6 }$ 
D)  $\frac { x ^ { 2 } } { x ^ { 2 } + 6 }$ 
E)  $\frac { 5 x ^ { 2 } } { x ^ { 2 } + 6 }$

Question 10

Determine $\lim _ { x \rightarrow 1 } f ( x )$ where $f ( x ) = \left\{ \begin{array} { l } 
10 - x ^ { 2 } , x \leq 1 \
7 - x , x > 1
\end{array} \right.$ (if it exists)by evaluating the corresponding one-sided limits.

Accepted Answer

A) 9 
B) 6 
C) 10 
D) 7 
E) limit does not exist 
A) 9 
B) 6 
C) 10 
D) 7 
E) limit does not exist

Question 11

Evaluate the sum using the summation formula and property. 
 $\sum _ { i = 1 } ^ { 30 } i ^ { 2 }$

Accepted Answer

A) 9,355 
B) 9,455 
C) 9,655 
D) 9,255 
E) 9,555 
A) 9,355 
B) 9,455 
C) 9,655 
D) 9,255 
E) 9,555

Question 12

Find $\lim _ { x \rightarrow + \infty } \left[ \frac { x } { ( 3 + x ) ^ { 2 } } - 4 \right]$ (if it exists).

Accepted Answer

A)   $- \frac { 1 } { 3 }$ 
B) 4 
C) -4 
D)  $\infty$ 
E) does not exist 
A)   $- \frac { 1 } { 3 }$ 
B) 4 
C) -4 
D)  $\infty$ 
E) does not exist

Question 13

Select the correct graph of the following function.  $f ( x ) = 5 x - \sqrt { 25 x ^ { 2 } + 3 }$

Accepted Answer

A)    
B)    
C)    
D)     
E)    
A)    
B)    
C)    
D)     
E)

Question 14

Find the limit by direct substitution.Round your answer to two decimal places.   $\lim _ { x \rightarrow 1 } e ^ { 3 x }$

Accepted Answer

A)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = 8103.08 
B)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = 2.72 
C)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = $\infty$ 
D)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = 20.09 
E)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = -20.09 
A)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = 8103.08 
B)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = 2.72 
C)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = $\infty$ 
D)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = 20.09 
E)  $\lim _ { x \rightarrow 1 } e ^ { 3 x }$ = -20.09

Question 15

Evaluate the sum using the summation formula and property. 
 $\sum _ { k = 1 } ^ { 10 } \left( k ^ { 3 } + 9 \right)$

Accepted Answer

A) 3,015 
B) 3,315 
C) 3,215 
D) 2,915 
E) 3,115 
A) 3,015 
B) 3,315 
C) 3,215 
D) 2,915 
E) 3,115

Question 16

Find the limit 
 $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }$

Accepted Answer

A)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 5$ 
B)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 4$ 
C)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 3$ 
D)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 5$ 
E)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 3$ 
A)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 5$ 
B)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 4$ 
C)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 3$ 
D)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = - 5$ 
E)  $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x } = 3$

Question 17

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result.   $h ( x ) = 5 x + 7 , \quad ( - 1,2 )$

Accepted Answer

A)  $m = - 7$ 
B)  $m = 7$ 
C)  $m = 4$ 
D)  $m = 5$ 
E)  $m = - 2$ 
A)  $m = - 7$ 
B)  $m = 7$ 
C)  $m = 4$ 
D)  $m = 5$ 
E)  $m = - 2$

Question 18

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ .  $f ( x ) = 5 \sqrt { x }$

Accepted Answer

A)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 5 } { 2 \sqrt { x } }$ 
B)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \frac { 7 } { 2 \sqrt { x } }$ 
C)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \frac { 3 } { 2 \sqrt { x } }$ 
D)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \frac { 5 } { 2 \sqrt { x } }$ 
E)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 7 } { 2 \sqrt { x } }$ 
A)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 5 } { 2 \sqrt { x } }$ 
B)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \frac { 7 } { 2 \sqrt { x } }$ 
C)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \frac { 3 } { 2 \sqrt { x } }$ 
D)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = \frac { 5 } { 2 \sqrt { x } }$ 
E)  $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h } = - \frac { 7 } { 2 \sqrt { x } }$

Question 19

Find the limit by direct substitution.   $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$

Accepted Answer

A)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $\frac { 1 } { 19 }$ 
B)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = -19 
C)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $\infty$ 
D)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $\frac { 19 } { 2 }$ 
E)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $- \frac { 2 } { 19 }$ 
A)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $\frac { 1 } { 19 }$ 
B)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = -19 
C)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $\infty$ 
D)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $\frac { 19 } { 2 }$ 
E)  $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$ = $- \frac { 2 } { 19 }$

Question 20

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result.   $g ( x ) = 10 - 2 x , \quad ( 1,8 )$

Accepted Answer

A)  $m = 8$ 
B)  $m = - 2$ 
C)  $m = 10$ 
D)  $m = 7$ 
E)  $m = - 10$ 
A)  $m = 8$ 
B)  $m = - 2$ 
C)  $m = 10$ 
D)  $m = 7$ 
E)  $m = - 10$

The limit of a function as x approaches c does not exist if the function approaches $- 5$ from the left of c and 4 from the right of

Find $\lim _ { x \rightarrow + \infty } \frac { 1 - 2 x } { 1 + 3 x }$ (if it exists).

Find the limit (if it exists). $\lim _ { x \rightarrow \infty } \left( \frac { 32 x - 1 } { 4 x + 4 } \right)$

Find the derivative of the function. $h ( s ) = \frac { 1 } { \sqrt { s + 2 } }$

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. $h ( x ) = \sqrt { x },(4,2)$

Select the correct function for the graph using horizontal asymptotes as aids.

Find the derivative of the function. $f ( x ) = \frac { 1 } { x + 13 }$

Select the correct function for the graph using horizontal asymptotes as aids.

Determine $\lim _ { x \rightarrow 1 } f ( x )$ where $f ( x ) = \left\{ \begin{array} { l } 10 - x ^ { 2 } , x \leq 1 \\7 - x , x > 1\end{array} \right.$ (if it exists)by evaluating the corresponding one-sided limits.

Evaluate the sum using the summation formula and property. $\sum _ { i = 1 } ^ { 30 } i ^ { 2 }$

Find $\lim _ { x \rightarrow + \infty } \left[ \frac { x } { ( 3 + x ) ^ { 2 } } - 4 \right]$ (if it exists).

Select the correct graph of the following function. $f ( x ) = 5 x - \sqrt { 25 x ^ { 2 } + 3 }$

Find the limit by direct substitution.Round your answer to two decimal places. $\lim _ { x \rightarrow 1 } e ^ { 3 x }$

Evaluate the sum using the summation formula and property. $\sum _ { k = 1 } ^ { 10 } \left( k ^ { 3 } + 9 \right)$

Find the limit $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }$

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. $h ( x ) = 5 x + 7 , \quad ( - 1,2 )$

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = 5 \sqrt { x }$

Find the limit by direct substitution. $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. $g ( x ) = 10 - 2 x , \quad ( 1,8 )$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Filters

Exam 12: Limits and An Introduction To Calculus

The limit of a function as x approaches c does not exist if the function approaches −5- 5−5 from the left of c and 4 from the right of

Find lim⁡x→+∞1−2x1+3x\lim _ { x \rightarrow + \infty } \frac { 1 - 2 x } { 1 + 3 x }limx→+∞​1+3x1−2x​ (if it exists).

Find the limit (if it exists). lim⁡x→∞(32x−14x+4)\lim _ { x \rightarrow \infty } \left( \frac { 32 x - 1 } { 4 x + 4 } \right)limx→∞​(4x+432x−1​)

Find the derivative of the function. h(s)=1s+2h ( s ) = \frac { 1 } { \sqrt { s + 2 } }h(s)=s+2​1​

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. h(x)=x,(4,2)h ( x ) = \sqrt { x },(4,2)h(x)=x​,(4,2)

Select the correct function for the graph using horizontal asymptotes as aids.

Find the derivative of the function. f(x)=1x+13f ( x ) = \frac { 1 } { x + 13 }f(x)=x+131​

Select the correct function for the graph using horizontal asymptotes as aids.

Evaluate the sum using the summation formula and property. ∑i=130i2\sum _ { i = 1 } ^ { 30 } i ^ { 2 }∑i=130​i2

Find lim⁡x→+∞[x(3+x)2−4]\lim _ { x \rightarrow + \infty } \left[ \frac { x } { ( 3 + x ) ^ { 2 } } - 4 \right]limx→+∞​[(3+x)2x​−4] (if it exists).

Select the correct graph of the following function. f(x)=5x−25x2+3f ( x ) = 5 x - \sqrt { 25 x ^ { 2 } + 3 }f(x)=5x−25x2+3​

Find the limit by direct substitution.Round your answer to two decimal places. lim⁡x→1e3x\lim _ { x \rightarrow 1 } e ^ { 3 x }limx→1​e3x

Evaluate the sum using the summation formula and property. ∑k=110(k3+9)\sum _ { k = 1 } ^ { 10 } \left( k ^ { 3 } + 9 \right)∑k=110​(k3+9)

Find the limit lim⁡x→0sin⁡3xx\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }limx→0​xsin3x​

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. h(x)=5x+7,(−1,2)h ( x ) = 5 x + 7 , \quad ( - 1,2 )h(x)=5x+7,(−1,2)

Find lim⁡h→0f(x+h)−f(x)h\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }limh→0​hf(x+h)−f(x)​ . f(x)=5xf ( x ) = 5 \sqrt { x }f(x)=5x​

Find the limit by direct substitution. lim⁡x→4(x−1x2+8x+9)\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)limx→4​(x2+8x+9x−1​)

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. g(x)=10−2x,(1,8)g ( x ) = 10 - 2 x , \quad ( 1,8 )g(x)=10−2x,(1,8)

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Filters

The limit of a function as x approaches c does not exist if the function approaches $- 5$ from the left of c and 4 from the right of

Find $\lim _ { x \rightarrow + \infty } \frac { 1 - 2 x } { 1 + 3 x }$ (if it exists).

Find the limit (if it exists). $\lim _ { x \rightarrow \infty } \left( \frac { 32 x - 1 } { 4 x + 4 } \right)$

Find the derivative of the function. $h ( s ) = \frac { 1 } { \sqrt { s + 2 } }$

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. $h ( x ) = \sqrt { x },(4,2)$

Find the derivative of the function. $f ( x ) = \frac { 1 } { x + 13 }$

Evaluate the sum using the summation formula and property. $\sum _ { i = 1 } ^ { 30 } i ^ { 2 }$

Find $\lim _ { x \rightarrow + \infty } \left[ \frac { x } { ( 3 + x ) ^ { 2 } } - 4 \right]$ (if it exists).

Select the correct graph of the following function. $f ( x ) = 5 x - \sqrt { 25 x ^ { 2 } + 3 }$

Find the limit by direct substitution.Round your answer to two decimal places. $\lim _ { x \rightarrow 1 } e ^ { 3 x }$

Evaluate the sum using the summation formula and property. $\sum _ { k = 1 } ^ { 10 } \left( k ^ { 3 } + 9 \right)$

Find the limit $\lim _ { x \rightarrow 0 } \frac { \sin 3 x } { x }$

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. $h ( x ) = 5 x + 7 , \quad ( - 1,2 )$

Find $\lim _ { h \rightarrow 0 } \frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = 5 \sqrt { x }$

Find the limit by direct substitution. $\lim _ { x \rightarrow 4 } \left( \frac { x - 1 } { x ^ { 2 } + 8 x + 9 } \right)$

Use the limit process to find the slope of the graph of the function at the specified point.Use a graphing utility to confirm your result. $g ( x ) = 10 - 2 x , \quad ( 1,8 )$